{"id":176748,"date":"2016-02-03T03:00:00","date_gmt":"2016-02-03T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=45673b17f4fe07f68ccac9c7a63c2e7f"},"modified":"2016-02-03T03:00:00","modified_gmt":"2016-02-03T00:00:00","slug":"understanding-the-damped-shm-without-odes","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=176748","title":{"rendered":"Understanding the damped SHM without ODEs"},"content":{"rendered":"<p>Instead of solving ordinary differential equations (ODEs), the damped simple harmonic motion (SHM)<br \/>\nis surveyed qualitatively from basic mechanics and quantitatively by the instrumentality of a graph<br \/>\nof velocity against displacement. In this way, the condition ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0031-9120\/51\/2\/025006\/pedaa05c5ieqn001.gif] {$bgeqslant sqrt{4mk}~$} for<br \/>\nthe occurrence of the non-oscillating critical damping and heavy-damping is derived. Besides, we<br \/>\nprove in the under-damping, the oscillation is isochronous and the diminishing amplitude satisfies a<br \/>\nrule of \u2018constant ratio\u2019. All are done on a non-ODE basis.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Instead of solving ordinary differential equations (ODEs), the damped simple harmonic motion (SHM)<br \/>\nis surveyed qualitatively from basic mechanics and quantitatively by the instrumentality of a graph<br \/>\nof velocity against displacement. In this way, the &#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-176748","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/176748","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=176748"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/176748\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=176748"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=176748"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=176748"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}